I can give the history of the Complexity Conference cover which should be similar since Complexity and FOCS are both IEEE Computer Society conferences.
When Complexity, then known as Structure in Complexity Theory, took on IEEE sponsorship in 1987, an IEEE artist took a look at the papers and came up with the cover with various symbols from the text. Here is a scan of the 1990 cover.

When Eric Allender took over the conference he rightly eliminated the strange symbols from the cover and in 1998 what is now the current cover first appeared.

If you are a budding artist and wish to redesign the complexity proceedings cover, we are always welcome to possibilities. If your cover is approved by the conference committee, you will be well acknowledged in the proceedings and bask in the glory of knowing your art work will live on in offices of complexity theorists around the world for generations to come.